Problem: Chubby Yang is studying linear equations right now. He came up with a nice problem. In the problem you are given an n × n matrix W, consisting of integers, and you should find two n × n matrices A and B, all the following conditions must hold: 

  * Aij = Aji, for all i, j (1 ≤ i, j ≤ n); 
  * Bij = - Bji, for all i, j (1 ≤ i, j ≤ n); 
  * Wij = Aij + Bij, for all i, j (1 ≤ i, j ≤ n). 



Can you solve the problem?

Input

The first line contains an integer n (1 ≤ n ≤ 170). Each of the following n lines contains n integers. The j-th integer in the i-th line is Wij (0 ≤ |Wij| < 1717).

Output

The first n lines must contain matrix A. The next n lines must contain matrix B. Print the matrices in the format equal to format of matrix W in input. It is guaranteed that the answer exists. If there are multiple answers, you are allowed to print any of them.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 4.

Examples

Input

2
1 4
3 2


Output

1.00000000 3.50000000
3.50000000 2.00000000
0.00000000 0.50000000
-0.50000000 0.00000000


Input

3
1 2 3
4 5 6
7 8 9


Output

1.00000000 3.00000000 5.00000000
3.00000000 5.00000000 7.00000000
5.00000000 7.00000000 9.00000000
0.00000000 -1.00000000 -2.00000000
1.00000000 0.00000000 -1.00000000
2.00000000 1.00000000 0.00000000

Solution (in JAVA):

Solution:

import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class B393{
	static final boolean FILE_IO = false;
	static final String output_file = "output.txt";
	static final String input_file = "input.txt";

	public static void main(String[] args){
		InputReader in = new InputReader();
		PrintWriter out;
		if(FILE_IO){
			try{
				out = new PrintWriter(output_file);
			} catch(FileNotFoundException e){
				throw new RuntimeException(e);
			}
		} else {
			out = new PrintWriter(System.out);
		}
		final long start = System.currentTimeMillis();
		new Task1().solve(in, out);
		final long duration = System.currentTimeMillis()-start;
		out.close();
	}

	static class Task1{
		public void solve(InputReader in, PrintWriter out){
			int n=in.nextInt();
			double[][] w=new double[n][n];
			double[][] a=new double[n][n];
			double[][] b=new double[n][n];

			for(int i=0; i<n; i++)
				for(int j=0; j<n; j++)
					w[i][j] = in.nextDouble();

			for(int i=0; i<n; i++)
				for(int j=0; j<n; j++){
					a[i][j] = (w[i][j]+w[j][i])/2;
					b[i][j] = w[i][j] - a[i][j];
				}

			for(int i=0; i<n; i++){
				for(int j=0; j<n; j++){
					out.print(a[i][j]+" ");
				}
				out.println();
			}
			for(int i=0; i<n; i++){
				for(int j=0; j<n; j++){
					out.print(b[i][j]+" ");
				}
				out.println();
			}
		}
	}

	static class InputReader{
		private BufferedReader reader;
		private StringTokenizer tokenizer;
		
		public InputReader(){
			if(FILE_IO){
				try{
					reader = new BufferedReader(new FileReader(input_file));
				} catch(FileNotFoundException e){
					throw new RuntimeException(e);
				}
			} else {
				reader = new BufferedReader(new InputStreamReader(System.in));
			}
			tokenizer = null;
		}

		public String next(){
			while(tokenizer==null || !tokenizer.hasMoreTokens()){
				try{
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e){
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt(){
			return (int)Integer.parseInt(next());
		}

		public long nextLong(){
			return (long)Long.parseLong(next());
		}

		public double nextDouble(){
			return (double)Double.parseDouble(next());
		}

		public String nextLine(){
			String s = null;
			try{
				s = reader.readLine();
			} catch(Exception e){
				throw new RuntimeException(e);
			}
			return s;
		}
	}
}